Born in Kingston Township, Ontario on 30 September 1848, one of eleven children born to Irish immigrants Henry Armstrong and Letitia Perry. He worked for a lumber company at Ottawa from 1869 to 1872 then operated a general store for six years at Roblin, Ontario. He came to Manitoba in 1880 and settled at Portage la Prairie where, for four years, he conducted a grocery business. Selling the business, he returned to Ontario and served eight years as manager of the Napanee Mills, afterwards operating his own business at Napanee. He returned to Manitoba in late 1902, settling at Carman where he worked for the real estate business of S. P. Hinch. He withdrew from the company in 1906 when he was appointed deputy land registrar at Carman.

On 20 January 1874 he married Elizabeth Booth (?-1894) of Richmond Township, Ontario. He married again on 25 November 1897 to Helen Miller of Camden Township, Ontario. They had a son, Harold Miller Armstrong. Hamilton Armstrong was a Mason and a member of the Methodist church. He served on the Carman town council.